Constraining the output value range of a CNN independent of the loss function
You can limit the absolute values of the outputs by "punishing" large values in the loss function. This is done by adding an extra term to the loss function. 

For example, if your existing loss function is L(yhat, y) where yhat is the output and y the correct value, create a new loss function 

L'(yhat, y) = L(yhat,y) + max(0, ||yhat||1 - k) 

When the outputs are "small" the L1 norm of your output yhat is less than k and imposes no extra loss (keeping everything as before). However once the norm grows above k it starts to impose a loss that guides the training to reduce the absolute values of the outputs values.

You can also limit the values in the network itself by selecting a bounded activation function for the output, for example tanh or sigmoid. However, you need to pick an activation function that suits your problem.